If x + y + z = 6, then the value of (x - 1)3 + (y

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If x + y + z = 6, then the value of (x - 1)³ + (y - 2)³ + (z - 3)³ is

1. 3 (x – 1 ) (y – 2 ) (z – 3 )
2. 3xyz
3. (x – 1 ) (y – 2 ) (z – 3 )
4. 2 (x – 1 ) (y – 2 ) (z – 3 )

Correct Option: A

Using Rule 21,
If. a + b + c = 0, then a³ + b³ + c³ = 3abc
Here, x – 1 + y – 2 + z – 3 = x + y + z – 6
= 6 – 6 = 0
∴ (x - 1)³ + (y - 2)³ + (z - 3)³ = 3(x – 1 )(y – 2 )(z – 3 )